1. Field of the Invention
The present invention relates to a method for determining an integration initial value of a PID controller, especially to a method for determining an integration initial value of a PID controller, wherein the integration initial value is added to integrator of the PID controller when the temperature is approaching the set value, thus reducing steady state time and preventing temperature overshoot.
2. Description of Prior Art
The temperature control is extensively used for modern industry. The stable temperature control is essential in industry such as textile, dye, car lacquer in conventional industry, cool storage and cake making in food industry, optical disk manufacture and PCB manufacture in electronic industry.
The temperature control for a system is preferably performed to achieve set temperature rapidly without overshoot. However, actually dilemma is inevitable wherein overshoot occurs when the set temperature can be rapidly reached, the set temperature cannot be rapidly reached when the overshoot is to be suppressed.
The PID controller is often used for temperature control, wherein PID stands for proportion, integration and differentiation. The proportion control sets the output being proportional to error amount and the output is increased with larger error. The integration control is used to eliminate steady-state error and generates larger output when the error is large. The differentiation control can fast achieve steady state based on error variation. However, the prior art PID controller has difficulty to fast achieve set temperature without overshoot.
FIGS. 1 to 4 show the control principle, block diagram and curve for a prior art PID controller, wherein Kp (proportional constant), Ti (integration time) and Td (differentiation time) are parameters used for PID control and the error value is equal to set temperature subtracting actual temperature. The control output can be calculated based on formula (1) below:control output=[(1+1/TiS+TdS)×Kp]×error  (1)
The P parameter is proportional parameter and stands for a proportion relationship between output value and error value (set temperature subtracting actual temperature). The output is increased for large error value and the output value is decreased for smaller error value, as shown in FIG. 2. The output value can be calculated based on formula (2)y=100/PB×X+50
where Kp=100/PB, PB is proportion band, and Kp is proportional constant
50% indicates control output at error free condition.
The output value is 50% when the error amount is 0, it means the set temperature being equal to the actual temperature. The system does not have steady-state error when the temperature is stable in this value. In fact, the output value might be any value between 0% to 100% instead of 50% when the error value is 0. The output value might not be fixed value even for the same system and drifted with external environment. Therefore, the steady state condition cannot be achieved only by proportion control.
The D parameter is an adjustable parameter (Kp), wherein the temperature reaction is fast and the set temperature is liable to be exceeded when Kp is large; the temperature reaction is slow and the set temperature is not liable to be exceeded when Kp is small.
The I parameter is also referred to as integration parameter or integration control and is used to eliminate control error. The integration control is expressed as formula (3) when error is present in the temperature.y=Ki×∫Xdt+y0 ki=Kp×1/Ti,X is error value  (3)
In above formula, the error value for each second is added and then multiplied by a constant to obtain an output value y to eliminate temperature error. As shown in FIG. 3, the operation amount is increased due to integration when the error value is large. The integrator will not perform integration when error value is 0, namely, the measured temperature is equal to the set temperature.
In the I control of the prior art PID controller; the nitration is performed from 0 to the set temperature. Therefore, the I parameter control is a lengthy processing for obtaining stable temperature. As shown by the temperature verse integration time curve (Ti), the temperature may be dropped in the integration control process.